Bi-planar coils comprise windings arranged on two parallel planes, and the desired field is produced in some region between them. Shields can also be present, and these comprise further windings arranged on another pair of planes parallel to the primary planes and placed further out from the region of interest. The shields serve the dual purposes of isolating the primary coil from stray external magnetic fields, and of minimizing exterior fields generated by the coil.
In magnetic resonance imaging (MRI) applications that are a primary focus of this invention, a patient is placed in a strong and substantially homogeneous static magnetic field, causing the otherwise randomly oriented magnetic moments of the protons, in water molecules within the body, to precess around the direction of the applied field. The part of the body in the substantially homogeneous region of the overall magnetic field is then irradiated with radio-frequency (RF) energy, causing some of the protons to change their spin orientation. When the RF energy source is removed, the protons in the sample return to their original configuration, inducing measurable signal in a receiver coil tuned to the frequency of precession. This is the magnetic resonance (MR) signal. Most importantly, the frequency at which protons precess depends on the background magnetic field.
In MRI applications, the strong magnetic field is perturbed slightly by the presence of the patient's body. To correct for this effect, gradient and shim coils are used to adjust the magnetic field so as to generate the best possible final image. The field within the specified target volume (specified DSV) is usually represented in terms of spherical harmonics, and the impurities in the field are then represented in terms of the coefficients of an expansion in these harmonics. Gradient and shim coils are therefore designed to correct a perturbed magnetic field by producing a particular spherical harmonic that can be added to the background magnetic field, so as to cancel the effect of a certain harmonic caused by an impurity. There may be many such coils in an MRI device, each correcting for a particular spherical harmonic in the impurity.
Gradient coils also serve the function of linearly encoding precessional frequency with position and hence enabling Fourier image reconstruction to be achieved.
The design task for gradient and shim coils is therefore to determine the winding pattern of the coil such that the desired magnetic field will be produced in a designated region within the coil. In MRI applications, the coil is usually wound on a cylindrical former. This has certain advantages in terms of the quality of the image that is finally produced. A description of these conventional coils in magnetic resonance imaging may be found in the book by Jin (1999, Electromagnetic Analysis and Design in Magnetic Resonance Engineering, CRC Press, Boca Raton), for example. Possibly the best-known method for designing gradient and shim windings for cylindrical coils is the “target-field” approach taught by Turner (1986, A target field approach to optimal coil design, J. Phys. D: Appl. Phys. 19, 147–151; Electrical coils, U.S. Pat. No. 5,289,151). This technique specifies the desired “target” field inside the cylinder in advance, and then employs Fourier transform methods to calculate the current density on the surface of the coil that is required to generate the target magnetic field. The ill-conditioned nature normally expected from such an inverse problem is overcome by the Fourier transform technique, which essentially assumes that the coil formers are notionally infinite in length. In practice, however, this assumption can usually be circumvented with an appropriate choice of current-density function, which in turn sometimes requires the use of certain smoothing functions in the Fourier space.
A related method for designing coils has been advanced by Forbes, Crozier and Doddrell (Asymmetric zonal shim coils for magnetic resonance, U.S. Pat. No. 6,377,148) and Forbes and Crozier (2001, Asymmetric zonal shim coils for magnetic resonance applications, Med. Phys. 28, 1644–1651). This approach is intended to account for the true (finite) length of the coil explicitly, but likewise involves approximations based on the use of Fourier series. Nevertheless, it is capable of designing coils, for target fields located asymmetrically with respect to the coil length, in a very systematic fashion.
Coils of finite length can also be designed directly using the approach of Crozier and Doddrell (1993, Gradient-coil design by simulated annealing, J. Magn. Reson. A 103, 354–357). Here, the Biot-Savart law is used to calculate the magnetic field resulting directly from a collection of wires wound on a former. The inverse problem of arranging the wires to produce a desired target magnetic field inside the coil is solved using ‘simulated annealing’, which is a stochastic optimization strategy. The method is extremely robust and can accommodate many types of constraints easily, simply by adding them to the penalty function. On the other hand, it is possible that complicated magnetic fields (with tesseral components, for example) may be difficult to design by this method, particularly in view of the number of numerical iterations required in the simulated annealing technique.
In a series of three recent papers, a new method has been presented for designing conventional cylindrical coils in such a way that the exact finite-length geometry of the coil is accounted for, without approximation. This technique appears in Forbes and Crozier (A novel target-field method for finite-length magnetic resonance shim coils: Part 1 Zonal shims, J. Phys. D: Appl. Phys. 34, 3447–3455, 2001; Part 2 Tesseral shims, J. Phys. D: Appl. Phys. 35, 839–849, 2002; A novel target-field method for magnetic resonance shim coils: Part 3 Shielded gradient and shim coils, J. Phys. D: Appl. Phys. 36, 333–333, 2002.); see also Forbes and Crozier (Asymmetric tesseral shim coils for magnetic resonance, U.S. Pat. No. 6,664,879). In this approach, the Biot-Savart law is used for a current sheet distributed over the cylindrical surface of the coil former, and an inverse problem is solved, in which the resulting magnetic field is specified in advance (as a desired target field), and the required current density on the coil is found by solving an integral equation. As expected, the governing equations are so ill-conditioned as to be incapable of yielding a solution in the usual sense; however, this difficulty is overcome using a regularization approach similar to the Tikhonov method (see, for example, Delves and Mohamed, Computational Methods for Integral Equations, Cambridge University Press, Cambridge 1985, page 307). This approach works well in practice, and has been used to design a range of different cylindrical shim coils, with asymmetrically located target fields. Once the current-density sheet on the cylinder has been determined by this technique, a streamfunction method is immediately available for designing the complicated winding patterns automatically. Further details can be obtained from the tutorial article by Brideson, Forbes and Crozier (Determining complicated winding patterns for shim coils using stream functions and the target-field method, Concepts in Mag. Reson. 14, 9–18, 2002.)
A similar approach has been presented very recently by Green, Bowtell and Morris, and has been adapted to the design of ‘uni-planar’ coils (2002, Uniplanar gradient coils for brain imaging, Proc. Intl. Soc. Mag. Reson. Med. 10, p 819). A uni-planar coil consists simply of windings located on a single plane, and is intended for producing a desired gradient field in a small volume adjacent to the coil. Again, a strong motivation for this work is evidently the desire to create truly open MRI systems, as discussed above.
U.S. Pat. No. 5,977,771 (Single gradient coil configuration for MRI systems with orthogonal directed magnetic fields) and U.S. Pat. No. 6,262,576 (Phased array planar gradient coil set for MRI systems) also disclose a method for designing uni-planar coils, based on the use of Fourier transforms. Mathematically, this technique assumes that the plane of the coil is of infinite extent, but uses a smoothing technique (‘apodization’) to confine the current to a region of acceptable size.
Bi-planar coils consist of windings placed on parallel planes, and the magnetic field of interest is created in the space between them. They also offer the possibility of more open MRI systems. Some designs have been presented by Martens et al for insertable bi-planar gradient coils (1991, M. A. Martens, L. S. Petropoulos, R. W. Brown, J. H. Andrews, M. A. Morich and J. L. Patrick, Insertable biplanar gradient coils for magnetic resonance imaging, Rev. Sci. Instrum. 62, 2639–2645). These authors also assumed plates of infinite extent, so that a solution based on Fourier transforms was again available, and they computed some winding patterns for symmetric gradient coils. This type of approach was extended by Crozier et al to allow for the presence of shields exterior to the primary bi-planar coil (1995, S. Crozier, S. Dodd, K. Luescher, J. Field and D. M. Doddrell, The design of biplanar, shielded, minimum energy, or minimum power pulsed B0 coils, MAGMA, 3, 49–55). A similar technique has been used in U.S. Pat. No. 5,942,898 (Thrust balanced bi-planar gradient set for MRI scanners), so as also to incorporate the presence of an external secondary winding set of coils. In that method, the thrust forces on each coil set due to the presence of the other were minimized.
It is an aim of this invention to provide improved methods of designing bi-planar coils and bi-planar coils having improved properties for use in, for example, magnetic resonance imaging.